sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36864, base_ring=CyclotomicField(3072))
M = H._module
chi = DirichletCharacter(H, M([0,1239,1024]))
pari:[g,chi] = znchar(Mod(85,36864))
Modulus: | 36864 | |
Conductor: | 36864 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 3072 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | even |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ36864(13,⋅)
χ36864(61,⋅)
χ36864(85,⋅)
χ36864(133,⋅)
χ36864(157,⋅)
χ36864(205,⋅)
χ36864(229,⋅)
χ36864(277,⋅)
χ36864(301,⋅)
χ36864(349,⋅)
χ36864(373,⋅)
χ36864(421,⋅)
χ36864(445,⋅)
χ36864(493,⋅)
χ36864(517,⋅)
χ36864(565,⋅)
χ36864(589,⋅)
χ36864(637,⋅)
χ36864(661,⋅)
χ36864(709,⋅)
χ36864(733,⋅)
χ36864(781,⋅)
χ36864(805,⋅)
χ36864(853,⋅)
χ36864(877,⋅)
χ36864(925,⋅)
χ36864(949,⋅)
χ36864(997,⋅)
χ36864(1021,⋅)
χ36864(1069,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(8191,20485,4097) → (1,e(1024413),e(31))
a |
−1 | 1 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 |
χ36864(85,a) |
1 | 1 | e(3072215) | e(1536467) | e(3072739) | e(30722489) | e(25643) | e(1024667) | e(15361441) | e(1536215) | e(30722125) | e(384295) |
sage:chi.jacobi_sum(n)